Integrate product of heaviside function and function of x

[coverband]

How would you integrate product of heaviside function and function of x

i.e. int[f(x)H(x)dx]

Thanks

 

[mathman]

Are you looking for definite integral or indefinite?

For indefinite, the integral=0 for x < 0 and = the integral of f(x) for x > 0.

For definite integral, integral of f(x) with lower bound ≥ 0.

 

[coverband]

Thanks

The integral is $$\int_{0}^{2\pi} a^2(sint)^3H(-asint)dt$$

Help !?

 

[mathman]

If a > 0, integral is (π,2π), while for a < 0, integral is (0,π). In both cases the integrand is now without H.